Normal Approximations to the Binomial Distribution Section 4 Normal Approximations to the Binomial Distribution

Example A sociologist conducted interviews with 16 registered voters. Assume that half the voters on the list are Democrats. Let x = the number of Democrats selected n = 16 p = ½ p(x) = q = ½

For approximating a binomial probability with a normal probability A binomial random variable x may be thought of as having an approximately normal distribution if n is sufficiently large. Note: n is sufficiently large if np and nq are at least 5. When approximating a binomial probability with a normal probability, use the continuity correction.

Example Find the probability that between 30 and 35 of the next 50 births at a particular hospital will be boys.